Reflecting wall first-passage time

HardExpected Value Stochastic Processes~6m

A symmetric $\pm 1$ walk lives on $\{0,1,2,3,4\}$ . The wall at $0$ is reflecting - whenever the walk is at $0$ its next step goes to $1$ with certainty - and $4$ is absorbing. Starting at $0$ , what is the expected number of steps to reach $4$ ?

Show hints (2)+

Write $E_i = 1 + \tfrac12 E_{i-1} + \tfrac12 E_{i+1}$ for interior states, with $E_0 = 1 + E_1$ from the reflecting wall.
Solve the linear system down to $E_0$ .

Answer

Reveal answer →

Create a free account to see the full worked solution and track your progress.

Create a free account

Interview format: Hedge Fund Quant, Prop Trading

Reflecting wall first-passage time

Answer

Related questions